The theory of integral equations received a major impetus with the
publication in 1900 of Ivar Fredholm's paper, showing the analogy with
the solution of systems of linear equations and demonstrating the
utility of the theory for the proof of existence theorems to
boundary-value problems. A very rapid international reaction
followed. In this paper, we examine the work of Émile Picard in
this area, beginning in 1902, even before the publication of the
French version of Fredholm's paper. Picard's work was particularly
influential in France and Italy, and was propagated both through his
own lectures and via the textbook of Lalescu.

John Charles Fields (1863-1932) is best remembered today by
mathematicians as the man after whom the Fields Medal is named. Few
people realize the Canadian origin of what is arguably the most
prestigious award in mathematics. In this talk, I will present a
preliminary sketch of Fields' life and work. First we will discuss
Fields as a student; then Fields as researcher; and finally, in many
ways most importantly, Fields as a scientific organizer.

>From January 1915 to July 1916 the Cambridge mathematics student
F. P. White kept a detailed diary in which he freely recorded all
aspects of his life. During this period White came top in the
Mathematical Tripos, embarked on postgraduate research in applied
mathematics and appeared in front of several Appeal Tribunals as a
conscientious objector. White's diary not only includes vivid
descriptions of the mathematics he studied and the mathematicians with
whom he associated but it also provides an insight into the intellectual
environment of the Cambridge pacifist milieu (Bertrand Russell
et al.) to which he belonged.

In a 1770 paper, A. L. F. Meister gave a quite general definition of
"polygon", and introduced other important concepts (such as the
winding number of a curve or polygon about a point). His paper (in
the Novi Comm. Goetting.) had no immediate influence, although it is
mentioned much later by Moebius and others; most mentions misinterpret
the definition. The approach to polygons proposed independently by
L. Poinsot in 1809 became widely known and generally adopted, possibly
because he used it to find the four regular star polyhedra (usually
known as Kepler-Poinsot polyhedra); somewhat later A.-L. Cauchy proved that these are the only possible ones. As it turns
out, Poinsot's approach is internally inconsistent, needlessly
restrictive, and leads to many exceptions and loss of continuity in
the types of polygons and polyhedra. Meister's approach avoids these,
and can serve as the starting point of a general theory of polygons
and polyhedra, in a way that is very much in tune with modern research
of these topics. It is hard to understand why-despite its
shortcomings and inconsistencies-Poinsot's definition is still the
one relied on almost exclusively. The talk will describe the two
definitions, point out the problems with Poinsot's, and illustrate the
simplifications obtained by Meister's.

G. H. Hardy wrote in his Apology that ballistics and
aerodynamics are "repulsively ugly and intolerably dull" and also
expressed ethical concerns about the use of mathematics for military
purposes. Nevertheless, Hardy was largely an exception for his time,
as many of his contemporaries, including O. Veblen and Hardy's
long-time collaborator J. E. Littlewood, contributed to the science of
exterior ballistics, the application of mathematics to projectile
motion. This paper will look at significant work in mathematical
ballistics during the late 19th and early 20th centuries, focusing
especially on the influential theory of Turin professor F. Siacci and
the ideas Littlewood developed as a second lieutenant in the Royal
Garrison Artillery during World War I.

In the mid-nineteenth century, American mathematician Benjamin Peirce
related contemporary plant morphology to developing planetary theory
by extending the so-called "law of phylotaxis" that expressed the
arrangement of leaves on plants as a series of fractions. Peirce
discovered an identity between this arrangement and planetary
revolutions. His result, and its place in subsequent arguments,
illustrate one use of mathematics in a nineteenth-century scientific
environment based on the conviction of certainty in the universe.

The talk will look at the role of Canada in accommodating refugees
from the Nazi purge. This concerns on the one hand the mechanisms of
emigration where Canada had a particular function, for example in
securing re-entry visa to the United States. On the other hand, and
to a much smaller extent than the U.S., mathematics in Canada itself
profited from immigration, with the group theoretic school of Richard
Brauer in Toronto being the biggest success, although Brauer left for
the U.S. in 1948. Brauer's case will be examined in some detail
while others (Peter Scherk, Alexander Weinstein, Hans Schwerdtfeger,
Hans Heilbronn, and George Lorentz) will be mentioned passingly. The
cases of Schwerdtfeger and Heilbronn, who came respectively in 1957
and 1964 from Australia and England, shows the more indirect
consequences of the emigrations from Europe. To complete the picture
one would have to include second generation emigrants (children of
emigrants having their mathematical education in the New World) and
those coming after the war directly from Germany (G. Lorentz and
others) due to economic hardships and scientific isolation there. The
talk is part of a book on German refugee-mathematicians which came out
in 1998 in German and will be published in an extended English version
with Princeton University Press.

The Swedish mathematician Gösta Mittag-Leffler (1846-1927) studied
as a "post-doctoral" student in Paris with C. Hermite and in Berlin
with K. Weierstrass between the years of 1873 and 1876, when
Weierstrass published his influential Zur Theorie der
eindeutigen analytischen Funktionen. During this period of time,
Mittag-Leffler elaborated upon this work of Weierstrass' and proved
the now-familiar theorem (in present-day notation) associated with his
name:

Suppose W is an open set in the plane, AÌW, A
has no limit point in W, and to each aÎA there are
associated a positive integer m(a) and a rational function

Pa(z) =

m(a)åj=1

cj,a (z-a)-j.

Then there exists a meromorphic function fÎW, whose
principal part at each aÎA is Pa and which has no
other poles in W.

In this paper I will briefly present a background to the
Mittag-Leffler Theorem, including the work of Weierstrass
regarding entire functions. I will then discuss Mittag-Leffler's
extension of these results to the existence of a meromorphic function
with arbitrarily assigned principal parts. Finally, I will
investigate Hermite's reception of Mittag-Leffler's theorem through
their correspondence (of which Hermite's letters have survived) and
his addition of the Mittag-Leffler theorem to his lecture material.